Seen this a few times with BG systems, you can't select CH on it own. Daft I know but it's done to speed up the install. As said you could sort it out with a 240Vac/240Vac SPST relay or just wire in the HW off on the programme & NO or SAT on the cylinder stat, as it should be.
I think you've hit the nail on the head here. The system is fully pumped with a 3 port valve but there's no wire going to the programmer from the 3 port valve to say HW off. I don't think the wiring is in too much of a state - like you say, they've cut this corner to save time and the last owner of the house mustn't have been bothered. I wish you were in my area Delta as you sound like you know what you're talking about! Out of interest what do you call yourself? A heating engineer? Just asking as I'm having trouble finding someone to come out and sort it.
And what does DIA stand for?